Epidemics in Multipartite Networks: Emergent Dynamics

TL;DR

This paper investigates the complex dynamics of multi-virus epidemics in large, non-complete multipartite networks, deriving differential equations to analyze virus persistence and selection phenomena.

Contribution

It develops analytical methods to understand the qualitative behavior of virus spread in multipartite networks, extending previous work on fluid limits and structured dynamics.

Findings

Conditions for virus persistence identified

Natural selection phenomena observed in virus competition

Structured epidemic dynamics characterized

Abstract

Single virus epidemics over complete networks are widely explored in the literature as the fraction of infected nodes is, under appropriate microscopic modeling of the virus infection, a Markov process. With non-complete networks, this macroscopic variable is no longer Markov. In this paper, we study virus diffusion, in particular, multi-virus epidemics, over non-complete stochastic networks. We focus on multipartite networks. In companying work http://arxiv.org/abs/1306.6198, we show that the peer-to-peer local random rules of virus infection lead, in the limit of large multipartite networks, to the emergence of structured dynamics at the macroscale. The exact fluid limit evolution of the fraction of nodes infected by each virus strain across islands obeys a set of nonlinear coupled differential equations, see http://arxiv.org/abs/1306.6198. In this paper, we develop methods to analyze the qualitative behavior of these limiting dynamics, establishing conditions on the virus micro characteristics and network structure under which a virus persists or a natural selection phenomenon is observed.